Problem 127 - A Complete Resource Book in Chemistry for JEE Main

Question

Calculate the weight of copper that will be deposited at the cathode in the electrolysis of a \(0.2 \mathrm{M}\) solution of copper sulphate, when quantity of electricity, equal to the required to liberate \(2.24 \mathrm{~L}\) of hydrogen at STP from a \(0.1 \mathrm{M}\) aqueous sulphuric acid, is passed (Atomic mass of \(\mathrm{Cu}=63.5\) ) (a) \(6.35 \mathrm{~g}\) (b) \(3.17 \mathrm{~g}\) (c) \(12.71 \mathrm{~g}\) (d) \(63.5 \mathrm{~g}\)

Step-by-Step Solution

Answer

The mass of copper deposited is 6.35 g.

Step 1: Calculate Moles of Hydrogen

First, determine the number of moles of hydrogen gas that are liberated at STP. Use the fact that 1 mole of any gas occupies 22.4 L at STP. Given the volume of hydrogen gas is 2.24 L, the moles of hydrogen are calculated as follows:\[\text{Moles of } H_2 = \frac{2.24 \text{ L}}{22.4 \text{ L/mol}} = 0.1 \text{ moles}\]

Step 2: Calculate Electricity Required for Hydrogen

According to the chemical reaction for electrolysis of water (\(2H^{+} + 2e^{-} \rightarrow H_2\)), 1 mole of \(H_2\) requires 2 moles of electrons (or 2 Faradays of electricity). Therefore, 0.1 moles of \(H_2\) requires:\[\text{Electricity required} = 2 \times 0.1 = 0.2 \text{ Faradays}\]

Step 3: Relate Electricity to Copper Deposition

The chemical reaction for copper deposition in electrolysis is \(Cu^{2+} + 2e^{-} \rightarrow Cu\). Here, 1 mole of \(Cu\) requires 2 moles of electrons (or 2 Faradays). Thus, since we have 0.2 Faradays, we can deposit:\[0.1 \text{ moles of } Cu\]

Step 4: Calculate Mass of Deposited Copper

To find the mass of the deposited copper, use the atomic mass of copper (\(63.5 \text{ g/mol}\)). Multiply the moles of copper by its atomic mass:\[\text{Mass of } Cu = 0.1 \times 63.5 \text{ g/mol} = 6.35 \text{ g}\]

Step 5: Final Answer

The mass of copper deposited at the cathode is 6.35 g.

Key Concepts

Copper deposition

Copper deposition is a process that occurs during electrolysis, where copper ions ( ) are reduced to solid copper metal ( ) on a cathode. This transformation is essential in industries for copper refining and electroplating.

• During electrolysis, an electric current is passed through a copper sulphate solution ( ), where copper is deposited on the cathode.
• As the electric current flows, copper ions gain electrons ( ) at the cathode, resulting in the formation of solid copper.
• In this exercise, the copper ions in a 0.2 M copper sulphate solution undergo this process.

Understanding copper deposition helps with learning how electroplating works and is crucial for processes that require pure metallic layers, such as circuit board manufacturing.

Faraday's laws of electrolysis

Faraday's laws of electrolysis are fundamental principles that explain how mass and electricity are related in electrolytic reactions. First articulated by Michael Faraday, these laws help predict quantitative outcomes of electrolysis.

• First Law: The mass of a substance deposited or liberated during electrolysis is proportional to the total electric charge passed through the electrolyte.
• Second Law: When the same amount of electricity is passed through different electrolytes, the mass of substances deposited or liberated is proportional to their chemical equivalent weights.

In our exercise, Faraday's laws allow us to relate the electricity needed to deposit a specific mass of copper based on the charge needed to liberate 2.24 L of hydrogen. Knowing these laws provides the framework for calculating the deposition of various substances in different electrolytic conditions.

Atomic mass

The atomic mass of an element is a fundamental concept in chemistry, representing the average mass of one atom of an element, generally expressed in atomic mass units (amu). It is crucial for stoichiometric calculations in chemical reactions.

• In the case of copper ( ), its atomic mass is 63.5 g/mol.
• The atomic mass allows us to convert between the number of moles and the mass of an element.
• Utilizing the atomic mass of copper in our calculation, we determined that 0.1 moles of copper corresponds to a mass of 6.35 g.

Understanding atomic mass is vital for chemical equations and necessary calculations in chemistry, as it serves as a basis for comparing quantities of different elements.

Electrochemical equivalence

Electrochemical equivalence refers to the concept of how much of a substance one faraday of electricity will deposit or liberate during electrolysis. This is directly proportional to the equivalent weight of the substance involved.

• The equivalent weight of an element or compound is the mass that will combine with or displace 1 mole of electrons (or 1 mole of hydrogen atoms).
• To calculate electrochemical equivalence, knowledge about the required charge for deposition and the substance's equivalent weight is necessary.
• In our scenario, copper's electrochemical equivalence was used to predict how much copper would be deposited with the given 0.2 Faradays of charge.

Understanding electrochemical equivalence makes it easier to calculate changes in mass due to electrolysis, guiding practical applications of electroplating and refining metals.